Unless the tree is diseased (and therefore weakened) I see no reason for concern.

First, check your home owners insurance policy or call your agent to get the details of what your covered for and what your neighbor's responsibility is should the tree fall on your home. This way you can hit the ground running should this occur. Your home ins company will have a list of contractors and arborists for tree removal from your property and home repair. Second, take video and photos at different angles of the situation as it is now and of course of the tree down and damage to your home should it happen. Third, if you feel the situation as it stands now keeps you from the natural enjoyment of your property check your with local municipal authorities to see what courses of action you can take. Fourth and most important, have a nice friendly talk with you neighbor about your concerns. Your neighbor might not even be aware that such a concern exists and see what you can work out together to prevent this from happening or to preplan a course of action you can take together if the tree comes down on your house. I had on my property a sixty foot American Persimmon tree in my back garden. I after I had filled a bird feeder near it I walked back to the house on a fine clear windless day. When I got to the back door I turned around to see if there were any birds at the feeder all I saw was a mass of green. The tree had fallen. There was no sound no wind, nothing, it just gently fell flat with its root ball upended nothing broken and the reason for this occurence I have yet to figure out. So yes you can be concerned because anything can happen.

Another point to consider is which way the prevailing wind blows or at least which direction the really strong ones normally blow in. But healthy well rooted trees don't normally blow over.

Thanks to all who replied in an effort to assuage my fears. All of your advice has been helpful.
:)